Linear time-invariant systems of the formare considered. The problem is to find a control vectoru(t)that will drive the state of this system from a givenz(0) to some (not necessarily fixed) final statez(tf) in some (not necessarily fixed) timetfwhile minimizing a cost functional of the formThe original system is re-written in the form of a descriptor-variable system consisting of the equations diagIt is shown that there is a matrixsuch thatthus the original optimal control problem is equivalent to the following problem. Find a control vectoru(t)that drives the descriptor vectorx(t)from a given x(0) to somex(tf)while minimizingUsing the results of an earlier paper on optimal control of descriptor systems (Ibrahimet al.1988), necessary conditions are derived for the existence of minima of; the problem of finding sufficient conditions for the existence of minima ofis not considered. Various formulae are obtained for designing open-loop controls corresponding to three different terminal boundary conditions (tffixed,z(tf)=0;tffixed,z(tf) free;tffree,z(tf)=0). The problem of choosing the matrixQof the original cost functionalJis investigated in some detail.